Int. J. of Thermodynamics ISSN 1301-9724 Vol. 10 (No. 2), pp. 53-60, June 2007 Generation of Entropy in Spark Ignition Engines Bernardo Ribeiro, Jorge Martins*, António Nunes Universidade do Minho Departamento de Engenharia Mecânica 4800-058 – Guimarães – PORTUGAL [email protected] Abstract Recent engine development has focused mainly on the improvement of engine efficiency and output emissions. The improvements in efficiency are being made by friction reduction, combustion improvement and thermodynamic cycle modification. New technologies such as Variable Valve Timing (VVT) or Variable Compression Ratio (VCR) are important for the latter. To assess the improvement capability of engine modifications, thermodynamic analysis of indicated cycles of the engines is made using the first and second laws of thermodynamics. The Entropy Generation Minimization (EGM) method proposes the identification of entropy generation sources and the reduction of the entropy generated by those sources as a method to improve the thermodynamic performance of heat engines and other devices. A computer model created and implemented in MATLAB Simulink was used to simulate the conventional Otto cycle and the various processes (combustion, free expansion during exhaust, heat transfer and fluid flow through valves and throttle) were evaluated in terms of the amount of the entropy generated. An Otto cycle, a Miller cycle (over-expanded cycle) and a Miller cycle with compression ratio adjustment are studied using the referred model in order to evaluate the amount of entropy generated in each cycle. All cycles are compared in terms of work produced per cycle. Keywords: IC engines, Miller cycle, entropy generation, over-expanded cycle 1. Introduction work to pump air across the partially closed throttle valve. In the Miller cycle engine the load Several technologies are used for the is controlled by inlet valve timing, eliminating the thermodynamic improvement of internal throttle valve and the subsequent pumping losses combustion engines, such as VVT (Flierl and (Flierl and Kluting, 2000). A comparison between Kluting, 2000) or VCR (Drangel et al. (2002). To the Otto and Miller cycles was already presented evaluate the potential for thermodynamic in a theoretical study (Martins, 2004). In the same improvement of these and other technologies, study the Miller cycle was presented as an numerical studies must be performed using alternative to the conventional Otto cycle engine different tools. EGM (Drangel et al., 2002 and when used under part load conditions. A Bejan, 1996) is proposed as a tool for internal significant improvement to the Miller cycle may combustion engine improvement based on the be achieved if compression ratio adjustment is measurement of the entropy generated at several used in addition to valve timing variation. processes taking place with the engine operation. With these results it is possible to define The Miller cycle is different from the strategies for engine improvement, reducing the conventional Otto cycle engine for it has a longer amount of entropy generated.* expansion. This longer expansion is achieved using an effective shorter intake stroke. The Spark ignition internal combustion engines, intake valve, which in the Otto cycle closes running at low loads, have their thermal shortly after BDC, in the Miller cycle closes a efficiency reduced due to the effect of the throttle significant time before BDC (early intake valve valve that controls the engine load and by the fact closure - EIVC), creating a depression inside the that the compression starts at low pressure. Under cylinder (1-8 of Figure 1), or closes significantly part load conditions, engines use some of the after BDC (late intake valve closure - LIVC), expelling the air and fuel mixture back to the intake manifold (5-1 of Figure 2). The effect is to * Author to whom correspondence should be sent Int. J. of Thermodynamics, Vol. 10 (No.2) 53 start the compression (point 1 of Figure 1 and 2. Thermodynamic Engine Model Figure 2) after the compression starting point of An entropy generation analysis was applied the Otto cycle, which is near BDC. In fact, in the to internal combustion engines and an entropy Miller cycle the intake is always at atmospheric generation calculation model was developed. A pressure, and work is not used to pump the charge computer model capable of calculating the into the cylinder as in the Otto cycle. At the same entropy generation due to several processes time, pressure and temperature at the exhaust within the engine shows that the main entropy valve opening are lower, which means that a generators in an internal combustion engine are smaller amount of enthalpy of the exhaust gases is the combustion, free expansion of gas during lost during the exhaust process. exhaust and intake, heat transfer and fluid flow It was shown in a previous work (Martins, through valves (including the throttle valve). A 2004) that the Miller cycle only with intake valve scheme of this calculation model is presented in closure time variation brings some improvement Figure 3. This model is divided in a first law of to engine cycle efficiency. However the same thermodynamic model and a entropy generation cycle with a compression ratio adjustment brings model. a significant improvement to the thermal 1st law model efficiency of the theoretical cycle. The Wall Temperature dS gen due to compression ratio adjustment is made in order to Heat transfer ratio heat transfer maintain the same effective compression ratio, Engine geometry Intake /Exhaust dSgen due to free just to avoid knock onset. As the intake valve conditions (p, T, r, ...) expansion Cylinder conditions closure is delayed, the effective compression ratio (p, T, ...) of the engine decreases and the maximum Mass transfer ratio Cylinder mass dS due to temperature and pressure inside the cylinder caracteristics gen S combustion S òdSgen gen decrease, leading to less efficient cycles. This (cp, cv, r, R) Flow mass effect should be inverted by increasing the caracteristics dSgen due to flow through valves effective compression ratio. (cp , cv, r, R) dSgen due to Throttle valve 3 Figure 3. Computer model structure for entropy generation calculation. A single zone model is based on the first law of thermodynamics expressed as: Pressure dU = dQ - dW + hindmin - houtdmout (1) From (1) temperature can be calculated by 2 dT the integration of : dt 4 6 1 dm patm 5 dT cyl 7 8 mcylcv (T) + Tcv,m (T) = dt dt Volume dQ dV dm = - p + T c (T) i Figure 1. Miller cycle with EIVC. dt dt å i p i dt (2) 3 And pressure is calculated from the integration of: dp dV dm i dT V + p = T R i + R imi Û Pressure å å dt dt i dt i dt (3) dm i dT dV Tå Ri + åR imi - p 2 dp dt dt dt Û = i i dt V 4 6 where mcyl is the mass of working fluid p atm 5 1 dmi Volume trapped in the cylinder and is the flow rate dt of each species i through the valves. Figure 2. Miller cycle with LIVC. 54 Int. J. of Thermodynamics, Vol. 10 (No.2) In the model, heat from combustion is In the case of the free expansion process, the supplied using a Wiebe function (Heywood, lost work is calculated by the enthalpy of the 1988): engine gases: é m+1ù & m& m& æ q- q0 ö Sgen,enthalpy= å (h - h0 )- å (h - h0 ) xb = 1- exp ê- aç ÷ ú (4) T T Dq in 0 out 0 ëê è ø ûú (12) With a = 5 and m = 2, q0 is the spark time where h is the enthalpy of each chemical species at the beginning of combustion in crank angle and inducted or exhausted from the cylinder and h0 is Dq is the burning interval in crank angle. The the enthalpy of the same chemical species at heat release rate is given by: environment conditions, considering normal atmospheric conditions of pressure and dQ dx = Q b (5) temperature. dq r dq Entropy generated in a combustion process where: may be calculated using the adiabatic combustion Q = h m Q (6) chamber model. As there is no mass, heat or work R c f LHV transferred, any change in the system entropy and (Abd Alla, 2002) during the combustion process is directly caused by the process itself. Entropy generation due to h = h -1.6082 + 4.6509l - 2.0764l2 c c max( ) combustion can be calculated by the difference in (7) entropy of the combustion products and reactants: where, Blair (1999) hc max = 0.9 n n S& = m& s - m& s (13) To calculate the mass flow through the valve gen,comb å pi pi å ri ri two situations are considered depending on the i=1 i=1 flow regime (i.e. relation between the pressures where subscripts pi and ri are products and up and downstream). The flow rate through the reactants respectively, s is the entropy and m& is valve is given by (Heywood, 1988): the mass burning rate. 1/ 2 1 ì é g-1 ùü During the operation of the engine, heat is C A p æ p ö g ï 2g ê æ p ö g úï exchanged between the cylinder charge and the m& = D r u ç d ÷ í 1 - ç d ÷ ý 1/ 2 ç p ÷ g -1 ê ç p ÷ ú cylinder walls and then between the engine and (RTu ) è u ø ï ê è u ø úï îï ë ûþï the surrounding environment. Applying the second law of thermodynamics to the cylinder (8) results in: When the flow is choked, i.e. the flow speed & & equals the speed of sound: & Qw Qcyl Sgen,heat = - (14) g Tw Tcyl p æ 2 ö g-1 d £ ç ÷ (9) & & ç ÷ where Qw and Qcyl is the heat transferred from pu è g + 1ø the cylinder content to the cylinder walls.